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Datei: vect_fun_ops_rv.pvs   Sprache: PVS

Original von: PVS©

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     subset_algebra_def "measure_integration/")
    (open? const-decl "bool" topology "topology/")
    (metric_open? const-decl "bool" metric_space_def "metric_space/")
    (subset? const-decl "bool" sets nil)
    (ball const-decl "set[T]" metric_space_def "metric_space/")
    (sigma_algebra_union? const-decl "bool" subset_algebra_def
     "measure_integration/")
    (is_countable const-decl "bool" countability "sets_aux/")
    (subset_algebra_complement? const-decl "bool" subset_algebra_def
     "measure_integration/")
    (subset_algebra_empty? const-decl "bool" subset_algebra_def
     "measure_integration/")
    (member const-decl "bool" sets nil)
    (measurable_set? const-decl "bool" measure_space_def
     "measure_integration/")
    (Intersection_surjective name-judgement
     "(surjective?[setofsets[T], set[T]])" sets_lemmas nil)
    (Intersection_surjective name-judgement
     "(surjective?[setofsets[T], set[T]])" sets_lemmas_aux
     "measure_integration/")
    (finite_emptyset name-judgement "finite_set" finite_sets nil)
    (finite_emptyset name-judgement "finite_set[T]" countable_props
     "sets_aux/")
    (finite_emptyset name-judgement "finite_set[T]" countable_setofsets
     "sets_aux/")
    (finite_emptyset name-judgement "finite_set[real]" measure_space
     "measure_integration/")
    (emptyset_is_compact name-judgement
     "compact[real, (metric_induced_topology)]" convergence_aux
     "metric_space/")
    (emptyset_is_clopen name-judgement
     "clopen[real, (metric_induced_topology)]" convergence_aux
     "metric_space/")
    (subset_algebra_emptyset name-judgement "(borel?)" real_borel
     "measure_integration/")
    (real_minus_real_is_real application-judgement "real" reals nil))
   nil))
 (borel_independence 0
  (borel_independence-1 nil 3509204782
   ("" (skosimp)
    (("" (typepred "X!1")
      (("" (typepred "Y!1")
        (("" (typepred "g!1")
          (("" (typepred "h!1")
            (("" (expand "independent?")
              (("" (skosimp)
                (("" (expand "borel_function?")
                  (("" (expand "measurable_function?")
                    (("" (inst -3 "B2!1")
                      (("" (inst -4 "B1!1")
                        (("" (inst -1 "B2!1")
                          (("" (inst -2 "B1!1")
                            ((""
                              (inst -5 "inverse_image(g!1, B1!1)"
                               "inverse_image(h!1, B2!1)")
                              ((""
                                (case-replace
                                 "inverse_image(X!1, inverse_image(g!1, B1!1))=inverse_image(g!1 o X!1, B1!1)")
                                (("1"
                                  (case-replace
                                   "inverse_image(Y!1, inverse_image(h!1, B2!1))=inverse_image(h!1 o Y!1, B2!1)")
                                  (("1"
                                    (hide-all-but 1)
                                    (("1"
                                      (apply-extensionality :hide? t)
                                      (("1"
                                        (expand "inverse_image")
                                        (("1"
                                          (expand "o ")
                                          (("1"
                                            (expand "member")
                                            (("1" (propax) nil nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil)
                                 ("2"
                                  (hide-all-but 1)
                                  (("2"
                                    (apply-extensionality :hide? t)
                                    (("2"
                                      (expand "o ")
                                      (("2"
                                        (expand "inverse_image")
                                        (("2"
                                          (expand "member")
                                          (("2" (propax) nil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((random_variable nonempty-type-eq-decl nil probability_measure nil)
    (measurable_function? const-decl "bool" measure_space_def
     "measure_integration/")
    (S formal-const-decl "sigma_algebra" probability_space nil)
    (sigma_algebra nonempty-type-eq-decl nil subset_algebra_def
     "measure_integration/")
    (sigma_algebra? const-decl "bool" subset_algebra_def
     "measure_integration/")
    (setofsets type-eq-decl nil sets nil)
    (setof type-eq-decl nil defined_types nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number nonempty-type-decl nil numbers nil)
    (T formal-nonempty-type-decl nil probability_space nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (borel_function type-eq-decl nil borel_functions
     "measure_integration/")
    (borel_function? const-decl "bool" borel_functions
     "measure_integration/")
    (metric_induced_topology const-decl "setofsets[T]" metric_space_def
     "metric_space/")
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (independent? const-decl "bool" probability_space nil)
    (borel nonempty-type-eq-decl nil borel "measure_integration/")
    (borel? const-decl "sigma_algebra" borel "measure_integration/")
    (set type-eq-decl nil sets nil)
    (inverse_image const-decl "set[D]" function_image nil)
    (g!1 skolem-const-decl
     "borel_function[real, metric_induced_topology, real, metric_induced_topology]"
     probability_space nil)
    (B1!1 skolem-const-decl "borel[real, metric_induced_topology]"
     probability_space nil)
    (h!1 skolem-const-decl
     "borel_function[real, metric_induced_topology, real, metric_induced_topology]"
     probability_space nil)
    (B2!1 skolem-const-decl "borel[real, metric_induced_topology]"
     probability_space nil)
    (member const-decl "bool" sets nil)
    (borel_comp_measurable_is_measurable application-judgement
     "measurable_function[T, S]" probability_space nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (O const-decl "T3" function_props nil))
   shostak))
 (partial_sum_is_random_variable_TCC1 0
  (partial_sum_is_random_variable_TCC1-1 nil 3391354647
   ("" (subtype-tcc) nil nilnil nil))
 (partial_sum_is_random_variable 0
  (partial_sum_is_random_variable-1 nil 3352017383
   ("" (induct "n1")
    (("1" (expand "sigma")
      (("1" (skosimp)
        (("1" (typepred "XS!1(0)")
          (("1" (expand "random_variable?")
            (("1" (expand "sigma")
              (("1" (case-replace "(LAMBDA t: XS!1(0)(t))=XS!1(0)")
                (("1" (apply-extensionality :hide? t) nil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("2" (skosimp*)
      (("2" (inst - "XS!1")
        (("2" (expand "sigma" 1)
          (("2" (typepred "XS!1(1 + j!1)")
            (("2" (expand "random_variable?")
              (("2"
                (lemma "sum_measurable"
                 ("g1" "XS!1(1 + j!1)" "g2" "LAMBDA t:
                              sigma(0, j!1, LAMBDA n: XS!1(n)(t))"))
                (("1" (expand "+") (("1" (propax) nil nil)) nil)
                 ("2" (propax) nil nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((+ const-decl "[T -> real]" real_fun_ops "reals/")
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (measurable_function nonempty-type-eq-decl nil measure_space_def
     "measure_integration/")
    (sum_measurable judgement-tcc nil measure_space_def
     "measure_integration/")
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (nat_induction formula-decl nil naturalnumbers nil)
    (sigma def-decl "real" sigma "reals/")
    (T_high type-eq-decl nil sigma "reals/")
    (T_low type-eq-decl nil sigma "reals/")
    (<= const-decl "bool" reals nil)
    (OR const-decl "[bool, bool -> bool]" booleans nil)
    (random_variable? const-decl "bool" probability_measure nil)
    (random_variable nonempty-type-eq-decl nil probability_measure nil)
    (measurable_function? const-decl "bool" measure_space_def
     "measure_integration/")
    (S formal-const-decl "sigma_algebra" probability_space nil)
    (sigma_algebra nonempty-type-eq-decl nil subset_algebra_def
     "measure_integration/")
    (sigma_algebra? const-decl "bool" subset_algebra_def
     "measure_integration/")
    (setofsets type-eq-decl nil sets nil)
    (setof type-eq-decl nil defined_types nil)
    (T formal-nonempty-type-decl nil probability_space nil)
    (pred type-eq-decl nil defined_types nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil))
   shostak))
 (distribution_function_TCC1 0
  (distribution_function_TCC1-1 nil 3321775180
   ("" (expand "distribution_function?")
    (("" (inst + "lambda (t:T): 0")
      (("1" (skosimp)
        (("1" (expand "<=")
          (("1" (case-replace "0 <= x!1")
            (("1" (lemma "P_fullset" ("P" "P"))
              (("1" (expand "fullset") (("1" (assertnil nil)) nil))
              nil)
             ("2" (lemma "P_emptyset" ("P" "P"))
              (("2" (expand "emptyset") (("2" (assertnil nil)) nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (lemma "constant_is_measurable")
        (("2" (inst - "LAMBDA (t: T): 0")
          (("2" (expand "constant?")
            (("2" (expand "const_fun") (("2" (inst?) nil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((measurable_function? const-decl "bool" measure_space_def
     "measure_integration/")
    (S formal-const-decl "sigma_algebra" probability_space nil)
    (sigma_algebra nonempty-type-eq-decl nil subset_algebra_def
     "measure_integration/")
    (sigma_algebra? const-decl "bool" subset_algebra_def
     "measure_integration/")
    (setofsets type-eq-decl nil sets nil)
    (setof type-eq-decl nil defined_types nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (T formal-nonempty-type-decl nil probability_space nil)
    (random_variable nonempty-type-eq-decl nil probability_measure nil)
    (<= const-decl "(S)" probability_space nil)
    (P_emptyset formula-decl nil probability_measure nil)
    (emptyset const-decl "set" sets nil)
    (P formal-const-decl "probability_measure" probability_space nil)
    (probability_measure nonempty-type-eq-decl nil probability_measure
     nil)
    (probability_measure? const-decl "bool" probability_measure nil)
    (probability nonempty-type-eq-decl nil probability_measure nil)
    (nnreal type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (P_fullset formula-decl nil probability_measure nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (fullset const-decl "set" sets nil)
    (<= const-decl "bool" reals nil)
    (constant? const-decl "bool" const_fun_def "structures/")
    (const_fun const-decl "[S -> T]" const_fun_def "structures/")
    (constant_is_measurable judgement-tcc nil measure_space_def
     "measure_integration/")
    (distribution_function? const-decl "bool" probability_space nil))
   shostak))
 (invert_distribution 0
  (invert_distribution-1 nil 3352018678
   ("" (skosimp)
    (("" (expand "<")
      (("" (expand "distribution_function")
        (("" (expand "<=")
          (("" (lemma "P_complement" ("A" "{t | X!1(t) > x!1}"))
            (("1" (inst - "P")
              (("1" (expand ">")
                (("1" (lemma "complement_lt1" ("x" "x!1" "X" "X!1"))
                  (("1" (expand "<" -1)
                    (("1" (expand ">" -1)
                      (("1" (replace -1 -2)
                        (("1" (expand "<=" -2) (("1" (assertnil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (assert)
              (("2" (typepred "x!1)
                (("2" (expand "<") (("2" (propax) nil nil)) nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((< const-decl "(S)" probability_space nil)
    (<= const-decl "(S)" probability_space nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (>= const-decl "bool" reals nil)
    (nnreal type-eq-decl nil real_types nil)
    (<= const-decl "bool" reals nil)
    (probability nonempty-type-eq-decl nil probability_measure nil)
    (probability_measure? const-decl "bool" probability_measure nil)
    (probability_measure nonempty-type-eq-decl nil probability_measure
     nil)
    (P formal-const-decl "probability_measure" probability_space nil)
    (complement_lt1 formula-decl nil probability_space nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (P_complement formula-decl nil probability_measure nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (> const-decl "bool" reals nil)
    (measurable_function? const-decl "bool" measure_space_def
     "measure_integration/")
    (random_variable nonempty-type-eq-decl nil probability_measure nil)
    (T formal-nonempty-type-decl nil probability_space nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (setof type-eq-decl nil defined_types nil)
    (setofsets type-eq-decl nil sets nil)
    (sigma_algebra? const-decl "bool" subset_algebra_def
     "measure_integration/")
    (sigma_algebra nonempty-type-eq-decl nil subset_algebra_def
     "measure_integration/")
    (S formal-const-decl "sigma_algebra" probability_space nil)
    (distribution_function const-decl "probability" probability_space
     nil))
   shostak))
 (interval_distribution 0
  (interval_distribution-1 nil 3352019023
   ("" (skosimp*)
    (("" (assert)
      (("" (expand "distribution_function")
        (("" (skosimp)
          ((""
            (lemma "P_intersection" ("A" "x!1 < X!1" "B" "X!1 <= y!1"))
            (("" (inst - "P")
              (("" (replace -1 1)
                (("" (hide -1)
                  (("" (assert)
                    ((""
                      (case-replace
                       "union(x!1 < X!1, X!1 <= y!1) = fullset[T]")
                      (("1" (hide -1)
                        (("1" (lemma "P_fullset")
                          (("1" (inst - "P")
                            (("1" (replace -1)
                              (("1"
                                (lemma
                                 "P_complement"
                                 ("A" "x!1 < X!1"))
                                (("1"
                                  (inst - "P")
                                  (("1"
                                    (rewrite "complement_lt1" -1)
                                    (("1"
                                      (replace -1)
                                      (("1" (assertnil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil)
                       ("2" (hide 2)
                        (("2" (apply-extensionality 1 :hide? t)
                          (("2" (expand "fullset")
                            (("2" (expand "union")
                              (("2"
                                (expand "member")
                                (("2"
                                  (expand "<")
                                  (("2"
                                    (expand "<=" 1)
                                    (("2"
                                      (expand ">" 1)
                                      (("2"
                                        (flatten)
                                        (("2" (assertnil nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real_minus_real_is_real application-judgement "real" reals nil)
    (subset_algebra_intersection application-judgement "(S)"
     probability_space nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (P formal-const-decl "probability_measure" probability_space nil)
    (probability_measure nonempty-type-eq-decl nil probability_measure
     nil)
    (probability_measure? const-decl "bool" probability_measure nil)
    (probability nonempty-type-eq-decl nil probability_measure nil)
    (<= const-decl "bool" reals nil)
    (nnreal type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (fullset const-decl "set" sets nil)
    (union const-decl "set" sets nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (set type-eq-decl nil sets nil)
    (P_fullset formula-decl nil probability_measure nil)
    (subset_algebra_fullset name-judgement "(S)" probability_space nil)
    (measurable_fullset name-judgement "measurable_set[T, S]"
     probability_space nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (complement_lt1 formula-decl nil probability_space nil)
    (P_complement formula-decl nil probability_measure nil)
    (> const-decl "bool" reals nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (member const-decl "bool" sets nil)
    (nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (subset_algebra_union application-judgement "(S)" probability_space
     nil)
    (P_intersection formula-decl nil probability_measure nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (measurable_function? const-decl "bool" measure_space_def
     "measure_integration/")
    (random_variable nonempty-type-eq-decl nil probability_measure nil)
    (< const-decl "(S)" probability_space nil)
    (<= const-decl "(S)" probability_space nil)
    (T formal-nonempty-type-decl nil probability_space nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (setof type-eq-decl nil defined_types nil)
    (setofsets type-eq-decl nil sets nil)
    (sigma_algebra? const-decl "bool" subset_algebra_def
     "measure_integration/")
    (sigma_algebra nonempty-type-eq-decl nil subset_algebra_def
     "measure_integration/")
    (S formal-const-decl "sigma_algebra" probability_space nil)
    (distribution_function const-decl "probability" probability_space
     nil))
   shostak))
 (limit_distribution_TCC1 0
  (limit_distribution_TCC1-1 nil 3425001876
   ("" (skosimp)
    (("" (expand "distribution_function")
      (("" (replace -1)
        (("" (assert)
          (("" (hide -1)
            (("" (lemma "m_increasing_convergence")
              (("" (inst - "lambda (n:nat): X!1 <= x!1 - 1 / (1 + n)")
                (("1" (split -1)
                  (("1" (expand "x_converges?")
                    (("1" (expand "to_measure")
                      (("1" (expand "o") (("1" (propax) nil nil)) nil))
                      nil))
                    nil)
                   ("2" (hide 2)
                    (("2" (expand "increasing?")
                      (("2" (skosimp)
                        (("2" (expand "subset?")
                          (("2" (expand "<=" 1)
                            (("2" (expand "member")
                              (("2"
                                (skosimp)
                                (("2"
                                  (lemma
                                   "both_sides_div_pos_le2"
                                   ("py"
                                    "x!2+1"
                                    "px"
                                    "y!1+1"
                                    "pz"
                                    "1"))
                                  (("2" (assertnil nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (hide 2)
                  (("2" (skosimp)
                    (("2" (expand "measurable_set?")
                      (("2" (propax) nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((distribution_function const-decl "probability" probability_space
     nil)
    (posrat_div_posrat_is_posrat application-judgement "posrat"
     rationals nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (P formal-const-decl "probability_measure" probability_space nil)
    (probability_measure nonempty-type-eq-decl nil probability_measure
     nil)
    (probability_measure? const-decl "bool" probability_measure nil)
    (probability nonempty-type-eq-decl nil probability_measure nil)
    (<= const-decl "bool" reals nil)
    (to_measure const-decl "measure_type" generalized_measure_def
     "measure_integration/")
    (measure_type nonempty-type-eq-decl nil generalized_measure_def
     "measure_integration/")
    (measure? const-decl "bool" generalized_measure_def
     "measure_integration/")
    (extended_nnreal nonempty-type-eq-decl nil extended_nnreal
     "extended_nnreal/")
    (finite_measure nonempty-type-eq-decl nil generalized_measure_def
     "measure_integration/")
    (finite_measure? const-decl "bool" generalized_measure_def
     "measure_integration/")
    (nnreal type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number nonempty-type-decl nil numbers nil)
    (S formal-const-decl "sigma_algebra" probability_space nil)
    (sigma_algebra nonempty-type-eq-decl nil subset_algebra_def
     "measure_integration/")
    (sigma_algebra? const-decl "bool" subset_algebra_def
     "measure_integration/")
    (setofsets type-eq-decl nil sets nil)
    (setof type-eq-decl nil defined_types nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T formal-nonempty-type-decl nil probability_space nil)
    (m_increasing_convergence formula-decl nil measure_props
     "measure_integration/")
    (O const-decl "T3" function_props nil)
    (x_converges? const-decl "bool" extended_nnreal "extended_nnreal/")
    (increasing? const-decl "bool" fun_preds_partial "structures/")
    (subset? const-decl "bool" sets nil)
    (member const-decl "bool" sets nil)
    (nnint_plus_posint_is_posint application-judgement "posint"
     integers nil)
    (both_sides_div_pos_le2 formula-decl nil real_props nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (sequence type-eq-decl nil sequences nil)
    (measurable_set nonempty-type-eq-decl nil measure_space_def
     "measure_integration/")
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (set type-eq-decl nil sets nil)
    (measurable_set? const-decl "bool" measure_space_def
     "measure_integration/")
    (measurable_function? const-decl "bool" measure_space_def
     "measure_integration/")
    (random_variable nonempty-type-eq-decl nil probability_measure nil)
    (<= const-decl "(S)" probability_space nil)
    (X!1 skolem-const-decl "random_variable[T, S]" probability_space
     nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (x!1 skolem-const-decl "real" probability_space nil)
    (/= const-decl "boolean" notequal nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields
       nil))
   nil))
 (limit_distribution 0
  (limit_distribution-1 nil 3425001894
   ("" (skosimp*)
    (("" (assert)
      (("" (expand "distribution_function")
        (("" (case-replace "P(X!1 <= x!1)=P(X!1 = x!1)+P(X!1 < x!1)")
          (("1" (hide -1)
            (("1" (assert)
              (("1" (lemma "P_IUnion")
                (("1"
                  (inst - "P"
                   "LAMBDA (n:nat): X!1 <= x!1 - 1 / (1 + n)")
                  (("1" (split -1)
                    (("1"
--> --------------------

--> maximum size reached

--> --------------------

¤ Dauer der Verarbeitung: 1.17 Sekunden  (vorverarbeitet)  ¤





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